The X-ray Transform for a Generic Family of Curves and Weights
نویسنده
چکیده
We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves . We prove generic injectivity and a stability estimate under the condition that the conormal bundle of covers T M .
منابع مشابه
Synthesis and Characterization of Polyaniline-Polystyrene-Chitosan/Zinc Oxide Hybrid Nanocomposite
A hybrid nanocomposite composed of polyaniline-polystyrene-chitosan/zinc oxide was prepared via a simple in situ polymerization method. The synthesized copolymers were analyzed using Fourier Transform InfraRed (FT-IR), and UltraViolet-Visible (UV–Vis) spectroscopies, ThermoGravimetric Analysis (TGA), and Field Emission Scanning Electron Microscopy (FE-SEM), X-ray diffracti...
متن کاملA Note on Twists of (y^2=x^3+1)
‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with ...
متن کاملThe X-ray Transform and its Application in Nano Crystallography
In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...
متن کاملThe Weighted Doppler Transform
We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves Γ. This is a generalization of the attenuated Doppler transform. Uniqueness is proven for a generic set of weights and families of curves under a condition on the weight function. This condition is satisfied in particular if the w...
متن کاملSnCl4/nano-sawdust as an Efficient Bio-based Catalyst for the Synthesis of 2-Substituted Benzothiazoles and Benzimidazoles
SnCl4/nano-sawdust was prepared as a carbohydrate-based catalyst containing of tin bearing cellulose units. The catalyst was characterized by X-ray diffraction (XRD), fourier transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FESEM) and energy dispersive X-ray spectroscopy (EDS). The catalyst was applied successfully as a readily available, inexpensive, biodeg...
متن کامل